The Role of Diversification Risk in Financial Bubbles

Abstract

We present an extension of the Johansen-Ledoit-Sornette (JLS) model to include an additional pricing factor called the "Zipf factor", which describes the diversification risk of the stock market portfolio. Keeping all the dynamical characteristics of a bubble described in the JLS model, the new model provides additional information about the concentration of stock gains over time. This allows us to understand better the risk diversification and to explain the investors' behavior during the bubble generation. We apply this new model to two famous Chinese stock bubbles, from

Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model

“…Extensions have been proposed, essentially amounting to choose alternative forms of the crash hazard rate h(t) that replace expression (4). Let us mention the so-called second-order and third-order LPPL Landau models [25,26,[70][71][72], the Weierstrasstype LPPL model [73,74], the JLS model extended with second-order and third-order harmonics [19,34,75,76] and the JLS-factor model in which the LPPL bubble component is augmented by other financial risks factors [77,78]. We should also mention that a nonparametric estimation of the log-periodic power law structure has been developed to complement the above parametric calibrations [79].…”